Multi-Scale Analysis of Deformation and Failure of Superplastic Materials

The superplastic deformation is modeled within the continuum theory of viscoplasticity with an anisotropic yield function and a microstructure-based overstress function. Grain growth and cavitation are incorporated in the model and their effects on the superplastic flow stress are investigated. In addition, a new multi-scale stability criterion for superplastic deformation taking into account both geometrical (macroscopic) and microstructural features including grain growth and cavitation is presented. The new stability criterion is based on Hart’s stability criterion and is obtained by combining a modified microstructure-based constitute model for superplastic deformation with grain and cavitation evolution equations. The effects of void fraction, grain size, and strain rate sensitivity on the stability of superplastic deformation are examined. Variable strain rate optimum forming paths are derived from the stability criterion and optimum pressure profiles for superplastic blow forming are generated using FE analysis.